1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 169,890 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 169,880 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     92
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     14
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      7
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      1
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      8
## 108  2020-06-16          East of England      3
## 109  2020-06-17          East of England      7
## 110  2020-06-18          East of England      4
## 111  2020-06-19          East of England      7
## 112  2020-06-20          East of England      4
## 113  2020-06-21          East of England      3
## 114  2020-06-22          East of England      6
## 115  2020-06-23          East of England      5
## 116  2020-06-24          East of England      4
## 117  2020-06-25          East of England      1
## 118  2020-06-26          East of England      5
## 119  2020-06-27          East of England      6
## 120  2020-06-28          East of England      8
## 121  2020-06-29          East of England      4
## 122  2020-06-30          East of England      4
## 123  2020-07-01          East of England      2
## 124  2020-07-02          East of England      5
## 125  2020-07-03          East of England      0
## 126  2020-07-04          East of England      2
## 127  2020-07-05          East of England      0
## 128  2020-07-06          East of England      0
## 129  2020-03-01                   London      0
## 130  2020-03-02                   London      0
## 131  2020-03-03                   London      0
## 132  2020-03-04                   London      0
## 133  2020-03-05                   London      0
## 134  2020-03-06                   London      1
## 135  2020-03-07                   London      0
## 136  2020-03-08                   London      0
## 137  2020-03-09                   London      1
## 138  2020-03-10                   London      0
## 139  2020-03-11                   London      6
## 140  2020-03-12                   London      6
## 141  2020-03-13                   London     10
## 142  2020-03-14                   London     14
## 143  2020-03-15                   London     10
## 144  2020-03-16                   London     15
## 145  2020-03-17                   London     23
## 146  2020-03-18                   London     27
## 147  2020-03-19                   London     25
## 148  2020-03-20                   London     44
## 149  2020-03-21                   London     49
## 150  2020-03-22                   London     54
## 151  2020-03-23                   London     63
## 152  2020-03-24                   London     87
## 153  2020-03-25                   London    113
## 154  2020-03-26                   London    129
## 155  2020-03-27                   London    130
## 156  2020-03-28                   London    122
## 157  2020-03-29                   London    146
## 158  2020-03-30                   London    149
## 159  2020-03-31                   London    181
## 160  2020-04-01                   London    202
## 161  2020-04-02                   London    191
## 162  2020-04-03                   London    196
## 163  2020-04-04                   London    230
## 164  2020-04-05                   London    195
## 165  2020-04-06                   London    197
## 166  2020-04-07                   London    220
## 167  2020-04-08                   London    238
## 168  2020-04-09                   London    206
## 169  2020-04-10                   London    170
## 170  2020-04-11                   London    178
## 171  2020-04-12                   London    158
## 172  2020-04-13                   London    166
## 173  2020-04-14                   London    144
## 174  2020-04-15                   London    142
## 175  2020-04-16                   London    140
## 176  2020-04-17                   London    100
## 177  2020-04-18                   London    101
## 178  2020-04-19                   London    103
## 179  2020-04-20                   London     95
## 180  2020-04-21                   London     94
## 181  2020-04-22                   London    109
## 182  2020-04-23                   London     77
## 183  2020-04-24                   London     71
## 184  2020-04-25                   London     58
## 185  2020-04-26                   London     53
## 186  2020-04-27                   London     51
## 187  2020-04-28                   London     44
## 188  2020-04-29                   London     44
## 189  2020-04-30                   London     40
## 190  2020-05-01                   London     41
## 191  2020-05-02                   London     41
## 192  2020-05-03                   London     36
## 193  2020-05-04                   London     30
## 194  2020-05-05                   London     25
## 195  2020-05-06                   London     37
## 196  2020-05-07                   London     37
## 197  2020-05-08                   London     30
## 198  2020-05-09                   London     23
## 199  2020-05-10                   London     26
## 200  2020-05-11                   London     18
## 201  2020-05-12                   London     18
## 202  2020-05-13                   London     17
## 203  2020-05-14                   London     20
## 204  2020-05-15                   London     18
## 205  2020-05-16                   London     14
## 206  2020-05-17                   London     15
## 207  2020-05-18                   London      9
## 208  2020-05-19                   London     14
## 209  2020-05-20                   London     19
## 210  2020-05-21                   London     12
## 211  2020-05-22                   London     10
## 212  2020-05-23                   London      6
## 213  2020-05-24                   London      7
## 214  2020-05-25                   London      9
## 215  2020-05-26                   London     13
## 216  2020-05-27                   London      7
## 217  2020-05-28                   London      8
## 218  2020-05-29                   London      7
## 219  2020-05-30                   London     12
## 220  2020-05-31                   London      6
## 221  2020-06-01                   London     10
## 222  2020-06-02                   London      7
## 223  2020-06-03                   London      6
## 224  2020-06-04                   London      8
## 225  2020-06-05                   London      4
## 226  2020-06-06                   London      0
## 227  2020-06-07                   London      5
## 228  2020-06-08                   London      5
## 229  2020-06-09                   London      4
## 230  2020-06-10                   London      7
## 231  2020-06-11                   London      5
## 232  2020-06-12                   London      3
## 233  2020-06-13                   London      3
## 234  2020-06-14                   London      3
## 235  2020-06-15                   London      1
## 236  2020-06-16                   London      2
## 237  2020-06-17                   London      1
## 238  2020-06-18                   London      2
## 239  2020-06-19                   London      3
## 240  2020-06-20                   London      3
## 241  2020-06-21                   London      4
## 242  2020-06-22                   London      2
## 243  2020-06-23                   London      1
## 244  2020-06-24                   London      4
## 245  2020-06-25                   London      3
## 246  2020-06-26                   London      2
## 247  2020-06-27                   London      1
## 248  2020-06-28                   London      2
## 249  2020-06-29                   London      2
## 250  2020-06-30                   London      1
## 251  2020-07-01                   London      2
## 252  2020-07-02                   London      2
## 253  2020-07-03                   London      1
## 254  2020-07-04                   London      1
## 255  2020-07-05                   London      2
## 256  2020-07-06                   London      0
## 257  2020-03-01                 Midlands      0
## 258  2020-03-02                 Midlands      0
## 259  2020-03-03                 Midlands      1
## 260  2020-03-04                 Midlands      0
## 261  2020-03-05                 Midlands      0
## 262  2020-03-06                 Midlands      0
## 263  2020-03-07                 Midlands      0
## 264  2020-03-08                 Midlands      3
## 265  2020-03-09                 Midlands      1
## 266  2020-03-10                 Midlands      0
## 267  2020-03-11                 Midlands      2
## 268  2020-03-12                 Midlands      6
## 269  2020-03-13                 Midlands      5
## 270  2020-03-14                 Midlands      4
## 271  2020-03-15                 Midlands      5
## 272  2020-03-16                 Midlands     11
## 273  2020-03-17                 Midlands      8
## 274  2020-03-18                 Midlands     13
## 275  2020-03-19                 Midlands      8
## 276  2020-03-20                 Midlands     28
## 277  2020-03-21                 Midlands     13
## 278  2020-03-22                 Midlands     31
## 279  2020-03-23                 Midlands     33
## 280  2020-03-24                 Midlands     41
## 281  2020-03-25                 Midlands     48
## 282  2020-03-26                 Midlands     64
## 283  2020-03-27                 Midlands     72
## 284  2020-03-28                 Midlands     89
## 285  2020-03-29                 Midlands     92
## 286  2020-03-30                 Midlands     90
## 287  2020-03-31                 Midlands    123
## 288  2020-04-01                 Midlands    140
## 289  2020-04-02                 Midlands    142
## 290  2020-04-03                 Midlands    124
## 291  2020-04-04                 Midlands    151
## 292  2020-04-05                 Midlands    164
## 293  2020-04-06                 Midlands    140
## 294  2020-04-07                 Midlands    123
## 295  2020-04-08                 Midlands    186
## 296  2020-04-09                 Midlands    139
## 297  2020-04-10                 Midlands    127
## 298  2020-04-11                 Midlands    142
## 299  2020-04-12                 Midlands    139
## 300  2020-04-13                 Midlands    120
## 301  2020-04-14                 Midlands    116
## 302  2020-04-15                 Midlands    147
## 303  2020-04-16                 Midlands    102
## 304  2020-04-17                 Midlands    118
## 305  2020-04-18                 Midlands    115
## 306  2020-04-19                 Midlands     92
## 307  2020-04-20                 Midlands    107
## 308  2020-04-21                 Midlands     86
## 309  2020-04-22                 Midlands     78
## 310  2020-04-23                 Midlands    103
## 311  2020-04-24                 Midlands     79
## 312  2020-04-25                 Midlands     72
## 313  2020-04-26                 Midlands     81
## 314  2020-04-27                 Midlands     74
## 315  2020-04-28                 Midlands     68
## 316  2020-04-29                 Midlands     53
## 317  2020-04-30                 Midlands     56
## 318  2020-05-01                 Midlands     64
## 319  2020-05-02                 Midlands     51
## 320  2020-05-03                 Midlands     52
## 321  2020-05-04                 Midlands     61
## 322  2020-05-05                 Midlands     59
## 323  2020-05-06                 Midlands     59
## 324  2020-05-07                 Midlands     48
## 325  2020-05-08                 Midlands     34
## 326  2020-05-09                 Midlands     37
## 327  2020-05-10                 Midlands     42
## 328  2020-05-11                 Midlands     33
## 329  2020-05-12                 Midlands     45
## 330  2020-05-13                 Midlands     40
## 331  2020-05-14                 Midlands     37
## 332  2020-05-15                 Midlands     40
## 333  2020-05-16                 Midlands     34
## 334  2020-05-17                 Midlands     31
## 335  2020-05-18                 Midlands     34
## 336  2020-05-19                 Midlands     34
## 337  2020-05-20                 Midlands     36
## 338  2020-05-21                 Midlands     32
## 339  2020-05-22                 Midlands     27
## 340  2020-05-23                 Midlands     34
## 341  2020-05-24                 Midlands     19
## 342  2020-05-25                 Midlands     26
## 343  2020-05-26                 Midlands     33
## 344  2020-05-27                 Midlands     29
## 345  2020-05-28                 Midlands     28
## 346  2020-05-29                 Midlands     20
## 347  2020-05-30                 Midlands     20
## 348  2020-05-31                 Midlands     22
## 349  2020-06-01                 Midlands     20
## 350  2020-06-02                 Midlands     22
## 351  2020-06-03                 Midlands     24
## 352  2020-06-04                 Midlands     16
## 353  2020-06-05                 Midlands     21
## 354  2020-06-06                 Midlands     20
## 355  2020-06-07                 Midlands     17
## 356  2020-06-08                 Midlands     16
## 357  2020-06-09                 Midlands     18
## 358  2020-06-10                 Midlands     15
## 359  2020-06-11                 Midlands     13
## 360  2020-06-12                 Midlands     12
## 361  2020-06-13                 Midlands      6
## 362  2020-06-14                 Midlands     18
## 363  2020-06-15                 Midlands     12
## 364  2020-06-16                 Midlands     15
## 365  2020-06-17                 Midlands     10
## 366  2020-06-18                 Midlands     15
## 367  2020-06-19                 Midlands      9
## 368  2020-06-20                 Midlands     15
## 369  2020-06-21                 Midlands     13
## 370  2020-06-22                 Midlands     13
## 371  2020-06-23                 Midlands     17
## 372  2020-06-24                 Midlands     15
## 373  2020-06-25                 Midlands     17
## 374  2020-06-26                 Midlands      5
## 375  2020-06-27                 Midlands      4
## 376  2020-06-28                 Midlands      6
## 377  2020-06-29                 Midlands      6
## 378  2020-06-30                 Midlands      5
## 379  2020-07-01                 Midlands      6
## 380  2020-07-02                 Midlands      8
## 381  2020-07-03                 Midlands      3
## 382  2020-07-04                 Midlands      4
## 383  2020-07-05                 Midlands      4
## 384  2020-07-06                 Midlands      0
## 385  2020-03-01 North East and Yorkshire      0
## 386  2020-03-02 North East and Yorkshire      0
## 387  2020-03-03 North East and Yorkshire      0
## 388  2020-03-04 North East and Yorkshire      0
## 389  2020-03-05 North East and Yorkshire      0
## 390  2020-03-06 North East and Yorkshire      0
## 391  2020-03-07 North East and Yorkshire      0
## 392  2020-03-08 North East and Yorkshire      0
## 393  2020-03-09 North East and Yorkshire      0
## 394  2020-03-10 North East and Yorkshire      0
## 395  2020-03-11 North East and Yorkshire      0
## 396  2020-03-12 North East and Yorkshire      0
## 397  2020-03-13 North East and Yorkshire      0
## 398  2020-03-14 North East and Yorkshire      0
## 399  2020-03-15 North East and Yorkshire      2
## 400  2020-03-16 North East and Yorkshire      3
## 401  2020-03-17 North East and Yorkshire      1
## 402  2020-03-18 North East and Yorkshire      2
## 403  2020-03-19 North East and Yorkshire      6
## 404  2020-03-20 North East and Yorkshire      5
## 405  2020-03-21 North East and Yorkshire      6
## 406  2020-03-22 North East and Yorkshire      7
## 407  2020-03-23 North East and Yorkshire      9
## 408  2020-03-24 North East and Yorkshire      8
## 409  2020-03-25 North East and Yorkshire     18
## 410  2020-03-26 North East and Yorkshire     21
## 411  2020-03-27 North East and Yorkshire     28
## 412  2020-03-28 North East and Yorkshire     35
## 413  2020-03-29 North East and Yorkshire     38
## 414  2020-03-30 North East and Yorkshire     64
## 415  2020-03-31 North East and Yorkshire     60
## 416  2020-04-01 North East and Yorkshire     67
## 417  2020-04-02 North East and Yorkshire     75
## 418  2020-04-03 North East and Yorkshire    100
## 419  2020-04-04 North East and Yorkshire    105
## 420  2020-04-05 North East and Yorkshire     92
## 421  2020-04-06 North East and Yorkshire     96
## 422  2020-04-07 North East and Yorkshire    102
## 423  2020-04-08 North East and Yorkshire    107
## 424  2020-04-09 North East and Yorkshire    111
## 425  2020-04-10 North East and Yorkshire    117
## 426  2020-04-11 North East and Yorkshire     98
## 427  2020-04-12 North East and Yorkshire     84
## 428  2020-04-13 North East and Yorkshire     94
## 429  2020-04-14 North East and Yorkshire    107
## 430  2020-04-15 North East and Yorkshire     96
## 431  2020-04-16 North East and Yorkshire    103
## 432  2020-04-17 North East and Yorkshire     88
## 433  2020-04-18 North East and Yorkshire     95
## 434  2020-04-19 North East and Yorkshire     88
## 435  2020-04-20 North East and Yorkshire    100
## 436  2020-04-21 North East and Yorkshire     76
## 437  2020-04-22 North East and Yorkshire     84
## 438  2020-04-23 North East and Yorkshire     63
## 439  2020-04-24 North East and Yorkshire     72
## 440  2020-04-25 North East and Yorkshire     69
## 441  2020-04-26 North East and Yorkshire     65
## 442  2020-04-27 North East and Yorkshire     65
## 443  2020-04-28 North East and Yorkshire     57
## 444  2020-04-29 North East and Yorkshire     69
## 445  2020-04-30 North East and Yorkshire     57
## 446  2020-05-01 North East and Yorkshire     64
## 447  2020-05-02 North East and Yorkshire     48
## 448  2020-05-03 North East and Yorkshire     40
## 449  2020-05-04 North East and Yorkshire     49
## 450  2020-05-05 North East and Yorkshire     40
## 451  2020-05-06 North East and Yorkshire     51
## 452  2020-05-07 North East and Yorkshire     45
## 453  2020-05-08 North East and Yorkshire     42
## 454  2020-05-09 North East and Yorkshire     44
## 455  2020-05-10 North East and Yorkshire     40
## 456  2020-05-11 North East and Yorkshire     29
## 457  2020-05-12 North East and Yorkshire     27
## 458  2020-05-13 North East and Yorkshire     28
## 459  2020-05-14 North East and Yorkshire     31
## 460  2020-05-15 North East and Yorkshire     32
## 461  2020-05-16 North East and Yorkshire     35
## 462  2020-05-17 North East and Yorkshire     26
## 463  2020-05-18 North East and Yorkshire     30
## 464  2020-05-19 North East and Yorkshire     27
## 465  2020-05-20 North East and Yorkshire     22
## 466  2020-05-21 North East and Yorkshire     33
## 467  2020-05-22 North East and Yorkshire     22
## 468  2020-05-23 North East and Yorkshire     18
## 469  2020-05-24 North East and Yorkshire     26
## 470  2020-05-25 North East and Yorkshire     21
## 471  2020-05-26 North East and Yorkshire     21
## 472  2020-05-27 North East and Yorkshire     22
## 473  2020-05-28 North East and Yorkshire     21
## 474  2020-05-29 North East and Yorkshire     25
## 475  2020-05-30 North East and Yorkshire     20
## 476  2020-05-31 North East and Yorkshire     20
## 477  2020-06-01 North East and Yorkshire     17
## 478  2020-06-02 North East and Yorkshire     23
## 479  2020-06-03 North East and Yorkshire     23
## 480  2020-06-04 North East and Yorkshire     17
## 481  2020-06-05 North East and Yorkshire     18
## 482  2020-06-06 North East and Yorkshire     21
## 483  2020-06-07 North East and Yorkshire     14
## 484  2020-06-08 North East and Yorkshire     11
## 485  2020-06-09 North East and Yorkshire     12
## 486  2020-06-10 North East and Yorkshire     19
## 487  2020-06-11 North East and Yorkshire      7
## 488  2020-06-12 North East and Yorkshire      9
## 489  2020-06-13 North East and Yorkshire     10
## 490  2020-06-14 North East and Yorkshire     11
## 491  2020-06-15 North East and Yorkshire      9
## 492  2020-06-16 North East and Yorkshire     10
## 493  2020-06-17 North East and Yorkshire      9
## 494  2020-06-18 North East and Yorkshire     11
## 495  2020-06-19 North East and Yorkshire      6
## 496  2020-06-20 North East and Yorkshire      4
## 497  2020-06-21 North East and Yorkshire      4
## 498  2020-06-22 North East and Yorkshire      6
## 499  2020-06-23 North East and Yorkshire      7
## 500  2020-06-24 North East and Yorkshire     10
## 501  2020-06-25 North East and Yorkshire      3
## 502  2020-06-26 North East and Yorkshire      7
## 503  2020-06-27 North East and Yorkshire      3
## 504  2020-06-28 North East and Yorkshire      4
## 505  2020-06-29 North East and Yorkshire      2
## 506  2020-06-30 North East and Yorkshire      4
## 507  2020-07-01 North East and Yorkshire      1
## 508  2020-07-02 North East and Yorkshire      4
## 509  2020-07-03 North East and Yorkshire      2
## 510  2020-07-04 North East and Yorkshire      3
## 511  2020-07-05 North East and Yorkshire      1
## 512  2020-07-06 North East and Yorkshire      2
## 513  2020-03-01               North West      0
## 514  2020-03-02               North West      0
## 515  2020-03-03               North West      0
## 516  2020-03-04               North West      0
## 517  2020-03-05               North West      1
## 518  2020-03-06               North West      0
## 519  2020-03-07               North West      0
## 520  2020-03-08               North West      1
## 521  2020-03-09               North West      0
## 522  2020-03-10               North West      0
## 523  2020-03-11               North West      0
## 524  2020-03-12               North West      2
## 525  2020-03-13               North West      3
## 526  2020-03-14               North West      1
## 527  2020-03-15               North West      4
## 528  2020-03-16               North West      2
## 529  2020-03-17               North West      4
## 530  2020-03-18               North West      6
## 531  2020-03-19               North West      7
## 532  2020-03-20               North West     10
## 533  2020-03-21               North West     11
## 534  2020-03-22               North West     13
## 535  2020-03-23               North West     15
## 536  2020-03-24               North West     21
## 537  2020-03-25               North West     21
## 538  2020-03-26               North West     29
## 539  2020-03-27               North West     36
## 540  2020-03-28               North West     28
## 541  2020-03-29               North West     46
## 542  2020-03-30               North West     67
## 543  2020-03-31               North West     52
## 544  2020-04-01               North West     86
## 545  2020-04-02               North West     96
## 546  2020-04-03               North West     95
## 547  2020-04-04               North West     98
## 548  2020-04-05               North West    102
## 549  2020-04-06               North West    100
## 550  2020-04-07               North West    135
## 551  2020-04-08               North West    127
## 552  2020-04-09               North West    119
## 553  2020-04-10               North West    117
## 554  2020-04-11               North West    138
## 555  2020-04-12               North West    125
## 556  2020-04-13               North West    129
## 557  2020-04-14               North West    131
## 558  2020-04-15               North West    114
## 559  2020-04-16               North West    135
## 560  2020-04-17               North West     98
## 561  2020-04-18               North West    113
## 562  2020-04-19               North West     71
## 563  2020-04-20               North West     83
## 564  2020-04-21               North West     76
## 565  2020-04-22               North West     86
## 566  2020-04-23               North West     85
## 567  2020-04-24               North West     66
## 568  2020-04-25               North West     66
## 569  2020-04-26               North West     55
## 570  2020-04-27               North West     54
## 571  2020-04-28               North West     57
## 572  2020-04-29               North West     63
## 573  2020-04-30               North West     59
## 574  2020-05-01               North West     45
## 575  2020-05-02               North West     56
## 576  2020-05-03               North West     55
## 577  2020-05-04               North West     48
## 578  2020-05-05               North West     48
## 579  2020-05-06               North West     44
## 580  2020-05-07               North West     49
## 581  2020-05-08               North West     42
## 582  2020-05-09               North West     30
## 583  2020-05-10               North West     41
## 584  2020-05-11               North West     35
## 585  2020-05-12               North West     38
## 586  2020-05-13               North West     25
## 587  2020-05-14               North West     26
## 588  2020-05-15               North West     33
## 589  2020-05-16               North West     32
## 590  2020-05-17               North West     24
## 591  2020-05-18               North West     31
## 592  2020-05-19               North West     35
## 593  2020-05-20               North West     27
## 594  2020-05-21               North West     27
## 595  2020-05-22               North West     26
## 596  2020-05-23               North West     31
## 597  2020-05-24               North West     26
## 598  2020-05-25               North West     31
## 599  2020-05-26               North West     27
## 600  2020-05-27               North West     27
## 601  2020-05-28               North West     28
## 602  2020-05-29               North West     20
## 603  2020-05-30               North West     19
## 604  2020-05-31               North West     13
## 605  2020-06-01               North West     12
## 606  2020-06-02               North West     27
## 607  2020-06-03               North West     22
## 608  2020-06-04               North West     22
## 609  2020-06-05               North West     16
## 610  2020-06-06               North West     26
## 611  2020-06-07               North West     20
## 612  2020-06-08               North West     23
## 613  2020-06-09               North West     17
## 614  2020-06-10               North West     16
## 615  2020-06-11               North West     16
## 616  2020-06-12               North West     11
## 617  2020-06-13               North West     10
## 618  2020-06-14               North West     15
## 619  2020-06-15               North West     16
## 620  2020-06-16               North West     15
## 621  2020-06-17               North West     12
## 622  2020-06-18               North West     13
## 623  2020-06-19               North West      7
## 624  2020-06-20               North West     11
## 625  2020-06-21               North West      7
## 626  2020-06-22               North West     11
## 627  2020-06-23               North West     13
## 628  2020-06-24               North West     13
## 629  2020-06-25               North West     14
## 630  2020-06-26               North West      5
## 631  2020-06-27               North West      7
## 632  2020-06-28               North West      9
## 633  2020-06-29               North West      5
## 634  2020-06-30               North West      6
## 635  2020-07-01               North West      2
## 636  2020-07-02               North West      6
## 637  2020-07-03               North West      4
## 638  2020-07-04               North West      1
## 639  2020-07-05               North West      3
## 640  2020-07-06               North West      5
## 641  2020-03-01               South East      0
## 642  2020-03-02               South East      0
## 643  2020-03-03               South East      1
## 644  2020-03-04               South East      0
## 645  2020-03-05               South East      1
## 646  2020-03-06               South East      0
## 647  2020-03-07               South East      0
## 648  2020-03-08               South East      1
## 649  2020-03-09               South East      1
## 650  2020-03-10               South East      1
## 651  2020-03-11               South East      1
## 652  2020-03-12               South East      0
## 653  2020-03-13               South East      1
## 654  2020-03-14               South East      1
## 655  2020-03-15               South East      5
## 656  2020-03-16               South East      8
## 657  2020-03-17               South East      7
## 658  2020-03-18               South East     10
## 659  2020-03-19               South East      9
## 660  2020-03-20               South East     13
## 661  2020-03-21               South East      7
## 662  2020-03-22               South East     25
## 663  2020-03-23               South East     20
## 664  2020-03-24               South East     22
## 665  2020-03-25               South East     29
## 666  2020-03-26               South East     35
## 667  2020-03-27               South East     34
## 668  2020-03-28               South East     36
## 669  2020-03-29               South East     55
## 670  2020-03-30               South East     58
## 671  2020-03-31               South East     65
## 672  2020-04-01               South East     66
## 673  2020-04-02               South East     55
## 674  2020-04-03               South East     72
## 675  2020-04-04               South East     80
## 676  2020-04-05               South East     82
## 677  2020-04-06               South East     88
## 678  2020-04-07               South East    100
## 679  2020-04-08               South East     83
## 680  2020-04-09               South East    104
## 681  2020-04-10               South East     88
## 682  2020-04-11               South East     88
## 683  2020-04-12               South East     88
## 684  2020-04-13               South East     84
## 685  2020-04-14               South East     65
## 686  2020-04-15               South East     72
## 687  2020-04-16               South East     56
## 688  2020-04-17               South East     86
## 689  2020-04-18               South East     57
## 690  2020-04-19               South East     70
## 691  2020-04-20               South East     87
## 692  2020-04-21               South East     51
## 693  2020-04-22               South East     54
## 694  2020-04-23               South East     57
## 695  2020-04-24               South East     64
## 696  2020-04-25               South East     51
## 697  2020-04-26               South East     51
## 698  2020-04-27               South East     40
## 699  2020-04-28               South East     40
## 700  2020-04-29               South East     47
## 701  2020-04-30               South East     29
## 702  2020-05-01               South East     37
## 703  2020-05-02               South East     36
## 704  2020-05-03               South East     17
## 705  2020-05-04               South East     35
## 706  2020-05-05               South East     29
## 707  2020-05-06               South East     25
## 708  2020-05-07               South East     27
## 709  2020-05-08               South East     26
## 710  2020-05-09               South East     28
## 711  2020-05-10               South East     19
## 712  2020-05-11               South East     25
## 713  2020-05-12               South East     27
## 714  2020-05-13               South East     18
## 715  2020-05-14               South East     32
## 716  2020-05-15               South East     25
## 717  2020-05-16               South East     22
## 718  2020-05-17               South East     18
## 719  2020-05-18               South East     22
## 720  2020-05-19               South East     12
## 721  2020-05-20               South East     22
## 722  2020-05-21               South East     15
## 723  2020-05-22               South East     17
## 724  2020-05-23               South East     21
## 725  2020-05-24               South East     17
## 726  2020-05-25               South East     13
## 727  2020-05-26               South East     19
## 728  2020-05-27               South East     18
## 729  2020-05-28               South East     12
## 730  2020-05-29               South East     21
## 731  2020-05-30               South East      8
## 732  2020-05-31               South East     12
## 733  2020-06-01               South East     11
## 734  2020-06-02               South East     13
## 735  2020-06-03               South East     18
## 736  2020-06-04               South East     11
## 737  2020-06-05               South East     11
## 738  2020-06-06               South East     10
## 739  2020-06-07               South East     12
## 740  2020-06-08               South East      8
## 741  2020-06-09               South East     10
## 742  2020-06-10               South East     11
## 743  2020-06-11               South East      5
## 744  2020-06-12               South East      6
## 745  2020-06-13               South East      6
## 746  2020-06-14               South East      7
## 747  2020-06-15               South East      8
## 748  2020-06-16               South East     12
## 749  2020-06-17               South East      9
## 750  2020-06-18               South East      4
## 751  2020-06-19               South East      7
## 752  2020-06-20               South East      5
## 753  2020-06-21               South East      3
## 754  2020-06-22               South East      2
## 755  2020-06-23               South East      8
## 756  2020-06-24               South East      7
## 757  2020-06-25               South East      5
## 758  2020-06-26               South East      8
## 759  2020-06-27               South East      8
## 760  2020-06-28               South East      6
## 761  2020-06-29               South East      5
## 762  2020-06-30               South East      5
## 763  2020-07-01               South East      2
## 764  2020-07-02               South East      6
## 765  2020-07-03               South East      3
## 766  2020-07-04               South East      4
## 767  2020-07-05               South East      1
## 768  2020-07-06               South East      0
## 769  2020-03-01               South West      0
## 770  2020-03-02               South West      0
## 771  2020-03-03               South West      0
## 772  2020-03-04               South West      0
## 773  2020-03-05               South West      0
## 774  2020-03-06               South West      0
## 775  2020-03-07               South West      0
## 776  2020-03-08               South West      0
## 777  2020-03-09               South West      0
## 778  2020-03-10               South West      0
## 779  2020-03-11               South West      1
## 780  2020-03-12               South West      0
## 781  2020-03-13               South West      0
## 782  2020-03-14               South West      1
## 783  2020-03-15               South West      0
## 784  2020-03-16               South West      0
## 785  2020-03-17               South West      2
## 786  2020-03-18               South West      2
## 787  2020-03-19               South West      4
## 788  2020-03-20               South West      3
## 789  2020-03-21               South West      6
## 790  2020-03-22               South West      7
## 791  2020-03-23               South West      8
## 792  2020-03-24               South West      7
## 793  2020-03-25               South West      9
## 794  2020-03-26               South West     11
## 795  2020-03-27               South West     13
## 796  2020-03-28               South West     21
## 797  2020-03-29               South West     18
## 798  2020-03-30               South West     23
## 799  2020-03-31               South West     23
## 800  2020-04-01               South West     22
## 801  2020-04-02               South West     23
## 802  2020-04-03               South West     30
## 803  2020-04-04               South West     42
## 804  2020-04-05               South West     32
## 805  2020-04-06               South West     34
## 806  2020-04-07               South West     39
## 807  2020-04-08               South West     47
## 808  2020-04-09               South West     24
## 809  2020-04-10               South West     46
## 810  2020-04-11               South West     43
## 811  2020-04-12               South West     23
## 812  2020-04-13               South West     27
## 813  2020-04-14               South West     24
## 814  2020-04-15               South West     32
## 815  2020-04-16               South West     29
## 816  2020-04-17               South West     33
## 817  2020-04-18               South West     25
## 818  2020-04-19               South West     31
## 819  2020-04-20               South West     26
## 820  2020-04-21               South West     26
## 821  2020-04-22               South West     23
## 822  2020-04-23               South West     17
## 823  2020-04-24               South West     19
## 824  2020-04-25               South West     15
## 825  2020-04-26               South West     27
## 826  2020-04-27               South West     13
## 827  2020-04-28               South West     17
## 828  2020-04-29               South West     15
## 829  2020-04-30               South West     26
## 830  2020-05-01               South West      6
## 831  2020-05-02               South West      7
## 832  2020-05-03               South West     10
## 833  2020-05-04               South West     17
## 834  2020-05-05               South West     14
## 835  2020-05-06               South West     19
## 836  2020-05-07               South West     16
## 837  2020-05-08               South West      6
## 838  2020-05-09               South West     11
## 839  2020-05-10               South West      5
## 840  2020-05-11               South West      8
## 841  2020-05-12               South West      7
## 842  2020-05-13               South West      7
## 843  2020-05-14               South West      6
## 844  2020-05-15               South West      4
## 845  2020-05-16               South West      4
## 846  2020-05-17               South West      6
## 847  2020-05-18               South West      4
## 848  2020-05-19               South West      6
## 849  2020-05-20               South West      1
## 850  2020-05-21               South West      9
## 851  2020-05-22               South West      6
## 852  2020-05-23               South West      6
## 853  2020-05-24               South West      3
## 854  2020-05-25               South West      8
## 855  2020-05-26               South West     11
## 856  2020-05-27               South West      5
## 857  2020-05-28               South West     10
## 858  2020-05-29               South West      7
## 859  2020-05-30               South West      3
## 860  2020-05-31               South West      2
## 861  2020-06-01               South West      7
## 862  2020-06-02               South West      2
## 863  2020-06-03               South West      7
## 864  2020-06-04               South West      2
## 865  2020-06-05               South West      2
## 866  2020-06-06               South West      1
## 867  2020-06-07               South West      3
## 868  2020-06-08               South West      3
## 869  2020-06-09               South West      0
## 870  2020-06-10               South West      1
## 871  2020-06-11               South West      2
## 872  2020-06-12               South West      2
## 873  2020-06-13               South West      2
## 874  2020-06-14               South West      0
## 875  2020-06-15               South West      1
## 876  2020-06-16               South West      2
## 877  2020-06-17               South West      0
## 878  2020-06-18               South West      0
## 879  2020-06-19               South West      0
## 880  2020-06-20               South West      2
## 881  2020-06-21               South West      0
## 882  2020-06-22               South West      1
## 883  2020-06-23               South West      1
## 884  2020-06-24               South West      1
## 885  2020-06-25               South West      0
## 886  2020-06-26               South West      3
## 887  2020-06-27               South West      0
## 888  2020-06-28               South West      0
## 889  2020-06-29               South West      1
## 890  2020-06-30               South West      0
## 891  2020-07-01               South West      0
## 892  2020-07-02               South West      0
## 893  2020-07-03               South West      0
## 894  2020-07-04               South West      0
## 895  2020-07-05               South West      1
## 896  2020-07-06               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-07-07"

The completion date of the NHS Pathways data is Tuesday 07 Jul 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -11.9795   -3.4071   -0.2507    3.1457    7.2131  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.709e+00  6.119e-02   76.96   <2e-16 ***
## note_lag    1.359e-05  6.318e-07   21.50   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 19.61395)
## 
##     Null deviance: 9796.9  on 66  degrees of freedom
## Residual deviance: 1351.0  on 65  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  110.985283    1.000014
exp(confint(lag_mod))
##                 2.5 %     97.5 %
## (Intercept) 98.273493 124.920132
## note_lag     1.000012   1.000015

Rsq(lag_mod)
## [1] 0.8620943

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1590.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.2                         
## year           2020                        
## month          06                          
## day            22                          
## svn rev        78730                       
## language       R                           
## version.string R version 4.0.2 (2020-06-22)
## nickname       Taking Off Again

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.4.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.14             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.5.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.2         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-148      fs_1.4.2          webshot_0.5.2     httr_1.4.1       
##  [5] rprojroot_1.3-2   tools_4.0.2       backports_1.1.8   utf8_1.1.4       
##  [9] R6_2.4.1          mgcv_1.8-31       DBI_1.1.0         colorspace_1.4-1 
## [13] withr_2.2.0       gridExtra_2.3     tidyselect_1.1.0  sodium_1.1       
## [17] curl_4.3          compiler_4.0.2    cli_2.0.2         labeling_0.3     
## [21] matchmaker_0.1.1  scales_1.1.1      digest_0.6.25     foreign_0.8-80   
## [25] rmarkdown_2.3     pkgconfig_2.0.3   htmltools_0.5.0   dbplyr_1.4.4     
## [29] htmlwidgets_1.5.1 rlang_0.4.6       readxl_1.3.1      rstudioapi_0.11  
## [33] farver_2.0.3      generics_0.0.2    jsonlite_1.7.0    crosstalk_1.1.0.1
## [37] car_3.0-8         zip_2.0.4         kyotil_2019.11-22 magrittr_1.5     
## [41] Matrix_1.2-18     Rcpp_1.0.5        munsell_0.5.0     fansi_0.4.1      
## [45] viridis_0.5.1     abind_1.4-5       lifecycle_0.2.0   stringi_1.4.6    
## [49] yaml_2.2.1        carData_3.0-4     snakecase_0.11.0  MASS_7.3-51.6    
## [53] plyr_1.8.6        grid_4.0.2        blob_1.2.1        crayon_1.3.4     
## [57] lattice_0.20-41   cowplot_1.0.0     splines_4.0.2     haven_2.3.1      
## [61] hms_0.5.3         knitr_1.29        pillar_1.4.4      boot_1.3-25      
## [65] ggsignif_0.6.0    reprex_0.3.0      glue_1.4.1        evaluate_0.14    
## [69] data.table_1.12.8 modelr_0.1.8      vctrs_0.3.1       selectr_0.4-2    
## [73] cellranger_1.1.0  gtable_0.3.0      assertthat_0.2.1  xfun_0.15        
## [77] openxlsx_4.1.5    broom_0.5.6       rstatix_0.6.0     survival_3.1-12  
## [81] viridisLite_0.3.0 ellipsis_0.3.1